... two aircraft, one flying level across the field, another climbing after a missed approach, had an extremely near miss, in my estimation, less than 50 feet, before the lower pilot saw the higher aircraft and broke violently to the right in the darkness.

It is sometimes claimed that concept of a near miss would be better expressed as near hit. However, near is used in the phrase with the sense "close" (compare "near future", "near neighbour") rather than the sense "approximate" (compare "near certainty", "near standstill").